What is implicit (dy)/(dx),y^3=x^8 ?

The answer to implicit (dy)/(dx),y^3=x^8 is (dy)/(dx)=(8x^7)/(3y^2)

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implicit (dy)/(dx),y^3=x^8

implicit derivative

\frac{d y}{d x}, y^{3} = x^{8}

\frac{d y}{d x} = \frac{8 x ^{7}}{3 y ^{2}}

Solution steps

y^{3} = x^{8}

Treat

y

y (x)

Differentiate both sides:

3 y^{2} \frac{d y}{d x} = 8 x^{7}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{8 x ^{7}}{3 y ^{2}}

\frac{d y}{d x} = \frac{8 x ^{7}}{3 y ^{2}}

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\frac{d}{d x} (x^{9} ln (8 x))

\frac{d}{d x} (ln (\frac{4 x ^{4} sin ( - 7 x )}{3 x - 3}))

What is implicit (dy)/(dx),y^3=x^8 ?
The answer to implicit (dy)/(dx),y^3=x^8 is (dy)/(dx)=(8x^7)/(3y^2)